0.15 Repeating as a Fraction
What is 0.15 Repeating?
0.15 repeating, also written as 0.15̄, is a decimal number that has a repeating pattern of 15. This means that the digits 15 will continue to repeat indefinitely in a cyclical pattern. In other words, 0.15 repeating is an infinite, non-terminating decimal expansion.
Converting 0.15 Repeating to a Fraction
To convert 0.15 repeating to a fraction, we can use the following steps:
Step 1: Let x = 0.15̄
Let's assign the variable x to the decimal 0.15 repeating.
Step 2: Multiply both sides by 100
Multiply both sides of the equation by 100 to get rid of the decimal point.
100x = 15.15̄
Step 3: Subtract x from both sides
Subtract x from both sides of the equation to get:
99x = 15
Step 4: Divide both sides by 99
Divide both sides of the equation by 99 to solve for x.
x = 15/99
Simplifying the Fraction
The fraction 15/99 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3.
x = 5/33
The Result
Therefore, 0.15 repeating as a fraction is equal to 5/33.
This article has shown you the step-by-step process of converting 0.15 repeating to a fraction. The result is a simple and exact fraction, 5/33, which can be used in mathematical calculations and applications.
